Beach Day by Rodger Bliss
July 2024

Velocity of the Situation

Velocity of the Situation
Joshua was paddling his canoe upstream at at constant rate. After six miles, the wind blew his hat into the stream. Thinking that he had no chance to recover his hat, he continued upstream for six more miles before turning back. He continued rowing at the same rate on his return trip and overtook his hat at exactly the same spot where he began his journey eight hours earlier.

What was the velocity of the stream?

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9 guesses to Velocity of the Situation

  • Manjush

    Stream velocity is 1.125 m/hr

  • Sorry that is not the rate I have Manjush. Please keep trying!
    Justify your conclusion by explaining your math if you disagree.


    The magnitude of the stream’s velocity is 1 mph.

  • brent

    I agree with Manjush.
    The river flows at 1.125 mph
    The man’s paddle rate (in still water) is 3.375 mph
    So going up-stream he makes a headway of 2.25 mph
    In order to go 6 miles up-stream, it takes him 2:40 (2.66… hrs)
    His hat falls in the water here and will take 6 miles / 1.125 mph = 5:20 (5.33…) hrs to return to start point.
    Man paddles another 2:40 up-river (6 more miles) then turns around.
    With current the man travels at 3.375 + 1.125 = 4.5 mph
    The return trip (12 miles) takes 12 / 4.5 = 2:40.
    The total time on the river for the man is initial 2:40 + 2nd 2:40 + 2:40 return time = 8 hrs
    Time on river after losing hat = 2:40 + 2:40 = 5:20 – same amount of time it took the hat to return to start point, so they both reach at the exact time.

    What is the solution you have Dude?

  • Manjush

    thats exactly what I was thinking… thanks a lot for typing it up all..

    btw dude I verified the solution again..

    cant be anything else since the situation boils dn to two eqns..
    12/(CanSpd-StSpd) + 12/(CanSpd+StSpd) = 8
    6/StSpd = 6/(CanSpd-StSpd) + 12/(CanSpd+StSpd)

    and solving it gives 1.125

  • BORGS is the winner today, even though the two of us may be wrong. This is what I have:
    1 MPH. Joshua was rowing at a constant rate in relation to the water, and it took him eight hours to travel 24 miles. At the point where he lost his hat, he had been rowing for six miles, or two hours. To meet Joshua where he began his journey, the hat had to travel downstream six miles. Joshua didn’t reach the hat until after he had rowed the remaining 18 miles, or for six more hours. Thus, it took the hat six hours to travel six miles, carried by the stream velocity of 1 MPH.


    Both solutions can be considered correct depending on how you interpret Joshua rowing at a constant rate. If you assume that “rowing at the same rate” is relative to land then 1 mph is the correct solution. As this would mean the journey upstream took the same amount of time as the journey back downstream, and in which case the logic provided by Dude is correct.

    Alternatively, If Joshua’s paddle rate is the same relative to the stream, 1.125mph is correct as described by Manjush and brent.

  • brent

    I just noticed this one is listed as “For Kids” – and the solution Manjush provides may be above “kids” level.

    It is confusing, as even the solution dude lists says: “Joshua was rowing at a constant rate in relation to the water.”

    Maybe this riddle should be the same question, but Joshua is riding a bike at a constant rate, and the wind blows his hat back to where he started. How fast was the wind blowing the hat? Or should clearly state Joshua is rowing at a constant rate in relation to the shore.

    Thanks a lot for all the riddles Dude, great mental exercise.

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